Bold Diagrammatic Monte Carlo Study of $\phi^4$ Theory

TL;DR

This paper introduces a renormalized Bold Diagrammatic Monte Carlo method for studying strongly coupled quantum field theories, successfully analyzing 3D $^4$ theory and confirming a nontrivial IR fixed point without resummation.

Contribution

The paper develops a renormalized BDMC approach that efficiently studies strong coupling regimes in quantum field theories without sign problems or additional resummation.

Findings

Confirmed the existence of a nontrivial IR fixed point in 3D $^4$ theory.

Demonstrated convergence of the scheme using bold correlation functions.

No resummation needed due to the scheme's convergence.

Abstract

By incorporating renormalization procedure into Bold Diagrammatic Monte Carlo (BDMC), we propose a method for studying quantum field theories in the strong coupling regime. BDMC essentially samples Feynman diagrams using local Metropolis-type updates and does not suffer from the sign problem. Applying the method to three dimensional $\phi^4$ theory, we analyze the strong coupling limit of the theory and confirm the existence of a nontrivial IR fixed point in agreement with prior studies. Interestingly, we find that working with bold correlation functions as building blocks of the Monte Carlo procedure, renders the scheme convergent and no further resummation method is needed.